We examine a large class of infinite triple series and establish general summation formula. This is done by expressing the in terms definite integrals involving arctangent function that are evaluated turn closed forms. Numerous explicit formulae tabulated for whose values result elegant expressions as π, ln2 Catalan constant G.

This paper presents a novel technique for manipulating structures which represent infinite power series. When power series are implemented using lazy evaluation, many operations can be written as simple recursive procedures. For example, the programs to generate the series for the elementary transcendental functions are almost transliterations of the defining integral equations. However, a naiv...